Computer Modeling of Cement Paste Microstructure

The NIST three-dimensional cement hydration and microstructure development model has been described in detail previously [1]. For this study, initial 3-D cement images were created matching either the Bogue composition of the cement provided above (for chloride diffusion predictions) or those provided by Delagrave et al. [20] (for tritiated water diffusion). While the exact particle size distributions of the cements were unavailable, particle size distributions from a previous study [21] that most closely matched the measured Blaine surface areas [8,20] were utilized. Silica fume was modelled as one pixel (1 µm³) particles and the overall hydration volume was 100 x 100 x 100 µm or 1,000,000 pixel elements. Initial microstructures were created for the following conditions: water-to-solids ratios of 0.45 and 0.25 (with 0 % and 6 % silica fume replacement by mass), a w/c ratio of 0.3 (with 0 %, 3 %, 6 %, 10 %, and 20 % silica fume additions by mass), and a w/c ratio of 0.2 (with no silica fume). Hydration of the initial microstructures was then simulated at 20 ºC until matching the measured degree of hydration for comparison to the chloride ion diffusivity data [22] and to one set of tritiated water diffusivity data [23], and for 1000 cycles of hydration at 23 ºC for comparison to the tritiated water diffusivity data obtained from specimens which were cured for 3 months [20]. Relative diffusivities were then computed using an electrical analogy [17] and a previously developed and documented finite difference computer code [24]. Relative diffusivity is the ratio of the diffusivity of the diffusing species in the cement paste relative to its value when diffusing in bulk water (i.e., the inverse of the previously defined formation factor).

Two schools of thought exist concerning the pozzolanic reaction of silica fume within cement-based materials. If a global equilibrium is maintained, the silica fume should first react with all of the CH, and only when all of the CH is consumed, will the Ca/Si ratio of the C-S-H be reduced from its "average" value of 1.5-1.7 [25]. In the "local equilibrium" model, formation of a low Ca/Si ratio (e.g., 1.1) pozzolanic C-S-H occurs near the silica fume particles, while some CH may persist (albeit metastably) in locations "far" from any of the silica fume. The differences between these two models are summarized in Table 2. Based on the results of Sellevold et al. [9] and Lu et al. [10], we have chosen to implement the latter model in the NIST cement hydration and microstructure development model. Specifically, for the reaction of silica fume with CH and conventional C_1.7SH_4.0 gel, the following reactions are assumed in the model:

1.1CH + S + 2.8H C_1.1SH_3.9

C_1.7SH_4.0 + 0.5H C_1.1SH_3.9 + 0.6CH

with an assumed molar volume of 101.8 cm³/mole for the pozzolanic C_1.1SH_3.9 gel [26]. Lu et al. [10] have observed that for a w/c=0.21 (18 % silica fume addition) cement paste, the H/S molar ratio of the C-S-H decreases from 3.9 at 3 days to 2.1 at 28 days, but as a simplification, we shall here assume a constant ratio of 3.9 in the hydration model. This model with a constant H/S ratio has previously been successfully applied to predicting the adiabatic temperature rise in concretes containing silica fume [26].

 

Table 2: Reaction of Silica Fume with Portland Cement

% SF 0 %	"Global model" 20 %-25 % CH	"Local model" 20 %-25 % CH
Increasing up to about 15 % to 20 %	CH declines. C-S-H Ca/Si ratio remains at 1.7.	CH reaction is quantitatively less than theoretical, locally. Some C-S-H has Ca/Si ratio less than 1.7 but some high ratio material persists.
15 % to 20 %	All CH gone. C-S-H Ca/Si ratio is 1.7	A few % CH persists. C-S-H has variable Ca/Si ratio but mean value is < 1.7
> 15 % to 20 %	All CH gone. Ca/Si ratio of C-S-H decreases.	A little CH persists. Ca/Si ratio of C-S-H decreased but considerable "spread" of ratios occurs locally within material.

It should be noted that both of these pozzolanic reactions will contribute to a further reduction in the capillary porosity of cement pastes containing silica fume due to their consumption of capillary pore water. In the NIST model, the first reaction is assumed to occur at the silica fume particle surfaces when a diffusing CH species collides with a silica fume pixel [26]. Further, the conversion of conventional C-S-H to pozzolanic C-S-H shown in the second reaction is prohibited when the unreacted silica fume content falls below 1.3 % of the overall system volume. This cutoff value was selected to provide the best agreement with the experimentally measured chloride ion diffusivity for the w/c=0.3 system with a 3 % silica fume addition. For the 6 % and higher silica fume additions, this criterion is never reached as the silica fume remaining after "complete" hydration always exceeds the 1.3 % volume fraction. For the 0.3 w/c ratio simulated systems, and for all four different silica fume addition levels, approximately 50 % of the initial silica fume reacted during the first 976 model cycles of hydration (corresponding to the measured degree of cement hydration for the w/c=0.3, 0 % silica fume specimen, 0.71). This is in general agreement with the experimental results of Lu et al. [10], who measured degrees of reaction of silica fume on the order of 45 % for w/c=(0.18-0.3) cement pastes with silica fume additions between 6 % and 48 % hydrated for 60 days, and also observed the degree of reaction of the silica fume to be independent of silica fume content.